Question

Write the equation of the parabola with a focus (-1 4) and directrix y = 3

Answer 1

Parabola
4P(y-k)=(x-h)^2
where (h,k) is vertex
P is distance from vertex to focus which is also equalt to distance from vertex to directix

we plot those points and see it opens up (don't cross directix)
P is positive
from 4 to 3 is a distace of 1
1/2=1/2
P=1/2
3+1/2=3.5
the vertex is (-1,3.5)

4(1/2)(y-3.5)=(x+1)^2
2(y-3.5)=(x+1)^2

put in vertex form (solve for y)
divide both sides by 2
y-3.5=(1/2)(x+1)^2
add 3.5
y=$(1/2)(x+1)^{2}+3.5$